We assume that the sensors harvest energy from the environment. The energy arrivals at the sensors are modeled as independent Bernoulli processes \(e_k(t) \in \left\lbrace 0 ,1\right\rbrace \) , \(t = 1,2,\dots \)  (see, e.g., [1]}, [2]}) with rates \(\lambda _k\) , \(k\in \mathcal {K}\) .
Therefore, during each slot, sensor \(k\)  harvests one unit of energy with probability \(\lambda _k\) 
and stores the energy in a battery with a finite capacity \(B\) .
We denote the battery level of sensor \(k\)  at the beginning of slot \(t\)  by \(b_k(t)\) , where \({b_k(t) \in \lbrace 0,\ldots ,B\rbrace }\) .
